A purported spokesman for Islamist group Boko Haram claimed responsibility for a bombing of a church outside the capital Abuja and other violence which stoked fear and anger in Africa's most populous nation.

Nigeria's national security adviser blamed Boko Haram for the horrific attacks that saw worshippers killed as they were leaving church and burnt inside their cars.

Victims at the church outside the capital, where 35 were killed, ran toward a priest with dying pleas, including one man who was mortally wounded.

The series of attacks drew condemnation from the Vatican, the White House and several western countries.

Nigerian authorities were unable to prevent the latest attacks despite military crackdowns and claims of arrests of Boko Haram members in the country, roughly divided between a mainly Muslim north and mostly Christian south.

One attack saw a suicide bomber seek to ram a military convoy in front of a secret police building in the northeastern city of Damaturu, in an attack that killed the bomber and three security agents.

The area around the church blast outside the capital degenerated into further chaos after the attack, with angry youths starting fires and threatening to rush a nearby police station.

Police shot into the air to disperse them and closed a major highway. Emergency officials called for more ambulances as rescuers sought to evacuate the dead and wounded, before calm later returned to the area.

A Vatican spokesman labelled that attack an act of "blind hatred", and the United States and former colonial power Britain were among Western nations that also condemned the violence.

Other attacks included a bomb blast outside an evangelical church in the central city of Jos that killed a policeman, said a spokesman for the governor.

Another explosion targeted a church in the northeastern area of Gadaka on Christmas Eve, but no one was reported killed, while two other blasts hit the northeastern city of Damaturu on Christmas Day, including the suicide bombing.